(CNN) - Sen. Amy Klobuchar's nascent presidential campaign has been dogged by allegations that the Minnesota Democrat mistreated her Senate staff. In an interview with CNN's Poppy Harlow on Thursday, the senator admitted she "can always do better" with her staff, but said her toughness would be an asset on the world stage.

Klobuchar cast the reports of staff mistreatment as a positive for her ability to operative on the international stage as president, namely when dealing with Russian President Vladimir Putin.

"If you are a boss, you have to have high standards, and that is what I have always had. And that doesn't mean it's a popularity contest all the time," she said. "And so I've had high standards for myself, high standards for our staff, and mostly I'm going to have high standards for the country."

She added: "One can always do better, and that means you want to be sure that you are listening to people if they felt that something was unfair, or they felt bad about something. But I still think that you have to demand good product. When you're out there on the world stage and dealing with people like Vladimir Putin, yeah, you want someone who's tough. You want someone that demands the answers and that's going to get things done, and that's what I've done my whole life."

Former staffers -- nearly all anonymously -- have accused Klobuchar of creating a hostile work environment during her years in the Senate. Some have complained about how her office handled human resources issues, including paid family leave, where Klobuchar's office required employees who took 12 weeks of paid maternity and paternity leave to stay at the office for three times that time off once they returned. That policy has since been scrapped.

The environment, according to Legistorm, a site that tracks Capitol Hill's workforce, has led Klobuchar to have the largest annual turnover rate in the Senate at 36% between 2001 and 2016.

Klobuchar dispensed with the idea that the turnover in her office makes her similar to President Donald Trump, whose White House has been dogged by considerable turnover. And though the senator did not say the coverage of her staff treatment was sexist, she did suggest that journalists need to ensure coverage of male candidates' treatment of staff is the same way as female candidates.

"I'm responsible for myself," she said. "I think the media is going to have to decide as they go down this track and there's other candidates that get in the race and they hear other reports of people being tough or pushing people, they're going to have to ask the men the same questions that they ask the women, and that's going to be in the media."

Klobuchar announced her 2020 campaign at a snowy, freezing outdoor event in February, vaulting the three-term senator into the crowded -- and growing -- field of Democrats looking to run against Trump.

Klobuchar's announcement was distinctive: Snow blanketed the ground around her, piling up on her head as she announced her candidacy.

Trump, clearly watching the announcement, responded to Klobuchar's event, tweeting, "Amy Klobuchar announced that she is running for President, talking proudly of fighting global warming while standing in a virtual blizzard of snow, ice and freezing temperatures. Bad timing. By the end of her speech she looked like a Snowman(woman)!"

Klobuchar quickly shot back.

"I wonder how your hair would fare in a blizzard," she tweeted, adding the emoji of a snowman.

The exchange mimics how Klobuchar told CNN she would like to deal with Trump, should she win the Democratic nomination.

"You have to run against him, head on, of course," she said. "But you also... don't go down every single rabbit hole with him, because if you lose track of your optimistic economic agenda, then the voters who want to know what you're for and not just what you're for against, they don't get a fair shake. And one of the things he tries to do is to side track people into what he's talking about that day."

She added: "Sometimes you respond to him, especially when he is picking at core values or saying divisive things that divide people in this country, but sometimes you don't respond to him at all, let him go off and rant and rave about whatever he wants to. And then the third is to do it sometimes with humor, which is what I did the day that I announced."

The reality for Klobuchar, though, is that she is far more likely to be able to work with Trump than a host of other Democratic candidates who have run to the left in their 2020 bids. Klobuchar has touted being a pragmatic leader who is willing to work with Republicans when she can, noting that the president has signed a series of bills she worked on.

That background has led Klobuchar to be widely considered Republican's favorite Democrat in the Senate, with a number of lawmakers on the right touting her around her 2020 announcement.

To Klobuchar, the reason is simple: "I have looked at results, and it doesn't mean I agree with them. In fact, I disagree with them on a lot of things. But I've tried to work across the aisle in a civil way for one major reason and that is to do better for our country."

Does that mean Klobuchar, who said she still identifies as a progressive, will tout those laudatory quotes from Republicans?

"Well," Klobuchar said with a laugh. "I won't be featuring their quotes every place."

Klobuchar concluded the interview by reflecting on why she got into politics: Her daughter.

"Do you think you'd be running for president if it weren't for your daughter," Harlow asked.

"I don't think so, because that's how I got into politics," she said, noting that one of her first political fights was to get insurance companies to allow women more than 24 hours in the hospital after giving birth. "That really hooked me on public service, because I realized one, there was no one else speaking up except a few other moms across the country, and two, you can actually get things done, you can actually win."